Difference Between T-test and Z-test (With Table)

T-test vs Z-test

The key difference between T-test and Z-test lies in the fact that a T-test is used to determine a statistically significant difference between two sample groups that are independent in nature, whereas Z-test is used to determine the difference between means of two population when variance are given.

A T-test is best with the problems that have a limited sample size, whereas Z-test works best for the problems with large sample size.

A hypothesis refers to a conjecture which is to be accepted or rejected after further observation, investigation, and scientific experimentation.

T-test and z-test are terms common when it comes to the statistical testing of hypothesis in the comparison of two sample means.

Notably, the two tests are parametric procedures of hypothesis testing since they are both their variables are measured on an interval scale.

However, the two tests are different from each other, as shown in the discussions and chart below.

Notably, to apply the t-test, the sample size should not exceed thirty, and not below five.

Above thirty, it would be regarded to be large, and below five, it would be regarded to be too small.

On the other hand, in a z-test, all samples are assumed to be independent. The sample size is also assumed to be large.

Notably, a large sample size while conducting a test of hypothesis using the z-test should have the sample size exceed thirty.

Additionally, the distribution of z is assumed to be normal, with a mean of zero and a variance of one.

Use

While both tests are used in the comparison of population averages, the two tests differ in their use.

The t-test is useful in the determination of the availability of statistical significance between two independent sample datasets.

The t-test is suited for the test of the hypothesis of problems with limited sample size, that is, sample size less than thirty and with the population variance unknown.

On the other hand, the z-test is used to show the deviation of a data point from the average of a set of data.

Additionally, the z-test is used for data sets that have known the standard deviation. The data set’s sample size should also be large; that is, it should exceed thirty.

Frequently Asked Questions (FAQ) About T-test and Z-test

📹 ⚙ Is the Z score and Z-test the same?

Z Score is the number of standard deviations of particular value away from the mean.

Z- test denotes a uni-variate statistical analysis used to test the hypothesis that proportions from two independent samples differ a lot. It determines to what extent a data point is away from its mean of the data set, in standard deviation.

📹 What is Z in probability distribution?

Z denotes the normal distribution in the probability distribution. It is a normal continuous probability distribution and it is also known as Gaussian distribution.

F(z) is a normal distribution density which is called the bell curve because its shape looks like a bell.

📁 What does T-value mean?

The T value measures the size of the difference relative to variation in the sample data. The greater the value of T, the greater of evidence against the null hypothesis.

📁 What are the 3 types of T-tests?

The list of three types of T-tests is given below:

One sample T-test

Independent two-sample T-test

Paired sample T-test

One Sample T-test in this type of group we compare the mean or average of any group against the set average of the group. The value of the average can be theoretical or population.

Independent two-sample T-test this type of T-test is used to compare the means of two different samples.

E.g. this type of test can be used when we compare the average weight of male students to the average weight of female students. Provided, for this compare the number of males and females should be equal.

Paired Sample T-test Here we measure one group at two different times. We compare different means for a group under two different conditions or at two different times.

Let us understand this with the help of an example.

A manager thinks that the productivity of his employees is decreasing. So he decided to conduct a training program for them. So, how would he find the training worked or not.

Then he will compare the productivity of employees before and after the training. Here the manager comparing the employees at different times and conditions. This is the paired sample test.

Infographic

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Conclusion

Despite being nearly similar, the T-test and Z-test differ largely from their application.

The big difference remains to be the use of a T-test for small sample sizes and the z-test for larger sample sizes.

Additionally, the t-test is suitable when the population variance is unknown while testing for the hypothesis of a sample size whose population variance is known requires the z-test.

Therefore, one should be careful while choosing the perfect parameter for the test of the hypothesis.

Word Cloud for Difference Between T-test and Z-test

The following is a collection of the most used terms in this article on T-test and Z-test. This should help in recalling related terms as used in this article at a later stage for you.

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